Least Common Multiple (LCM) of 105 and 90
The least common multiple (LCM) of 105 and 90 is 630.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 105 and 90?
First, calculate the GCD of 105 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 90 = 1 remainder 15 |
| 2 | 90 ÷ 15 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 136 | 5032 |
| 131 and 82 | 10742 |
| 192 and 31 | 5952 |
| 20 and 39 | 780 |
| 49 and 178 | 8722 |